The foreign names like Georgia/Georgien may have something to do with the popularity of St. George among Georgians. Or maybe not. The predominantly Slavic name Gruzija (and similar) comes from the Russian word Gruziya.

(Abkhazia and South Ossetia do not want to be a part of Georgia, but officially still are, to most people. This is a serious problem, so don’t go there. Check what your Ministry of Foreign affairs has to say on the topic.)